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Prove of the complicated integral

  1. Jan 16, 2012 #1
    Hi experts!

    How to prove this integral?

    [itex]\frac{2}{e^{5}}[/itex][itex]\leq[/itex][itex]\int[/itex][itex]\int_{D}[/itex]e[itex]^{-(x^{2}+y^{2})}[/itex]dxdy[itex]\leq[/itex]2
    on
    D=[0,1] and [0,2]

    Here D is subscript of the 2nd integral.

    I seriously have no idea how to start. I am 100% blank with this question.

    Thanks in advance.
     
  2. jcsd
  3. Jan 16, 2012 #2

    micromass

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    What is the maximum/minimum value that [itex]e^{-(x^2+y^2)}[/itex] can attain??
     
  4. Jan 17, 2012 #3
    Why not just calculate the integral? The rectangle (0,1) x (0,2) is diffeomorphic to a circle (or the circle minus a set of measure zero) so use the change of variables theorem.
     
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